A new theory of regular functions of a quaternionic variable

In this paper we develop the fundamental elements and results of a new theory of regular functions of one quaternionic variable. The theory we describe follows a classical idea of Cullen, but we use a more geometric formulation to show that it is possible to build a rather complete theory. Our theor...

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Published in:	Advances in mathematics (New York. 1965) Vol. 216; no. 1; pp. 279 - 301
Main Authors:	Gentili, Graziano, Struppa, Daniele C.
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.12.2007
Subjects:	Functions of complex variables Functions of hypercomplex variables Quaternions Quaternions Functions of hypercomplex variables Functions of complex variables
ISSN:	0001-8708, 1090-2082
Online Access:	Get full text
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Abstract	In this paper we develop the fundamental elements and results of a new theory of regular functions of one quaternionic variable. The theory we describe follows a classical idea of Cullen, but we use a more geometric formulation to show that it is possible to build a rather complete theory. Our theory allows us to extend some important results for polynomials in the quaternionic variable to the case of power series.
AbstractList	In this paper we develop the fundamental elements and results of a new theory of regular functions of one quaternionic variable. The theory we describe follows a classical idea of Cullen, but we use a more geometric formulation to show that it is possible to build a rather complete theory. Our theory allows us to extend some important results for polynomials in the quaternionic variable to the case of power series.
Author	Gentili, Graziano Struppa, Daniele C.
Author_xml	– sequence: 1 givenname: Graziano surname: Gentili fullname: Gentili, Graziano email: gentili@math.unifi.it organization: Dipartimento di Matematica “U. Dini”, Università di Firenze, Viale Morgagni, 67 A, Firenze, Italy – sequence: 2 givenname: Daniele C. surname: Struppa fullname: Struppa, Daniele C. email: struppa@chapman.edu organization: Department of Mathematics and Computer Science, Chapman University, Orange, CA 92866, USA
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References	Gentili, Struppa (bib006) 2006; 342 Rinehart (bib012) 1960; 27 Sudbery (bib013) 1979; 85 Fueter (bib004) 1934; 7 Leutwiler (bib010) 1992; 20 Pogorui, Shapiro (bib011) 2004; 49 Kravchenko, Shapiro (bib007) 1996; vol. 351 Colombo, Sabadini, Sommen, Struppa (bib002) 2004 Fueter (bib005) 1939; 12 Laville, Ramadanoff (bib008) 1998; 8 Laville, Ramadanoff (bib009) 2001; 45 Ahlfors (bib001) 1966 Cullen (bib003) 1965; 32 Ahlfors (10.1016/j.aim.2007.05.010_bib001) 1966 Colombo (10.1016/j.aim.2007.05.010_bib002) 2004 Leutwiler (10.1016/j.aim.2007.05.010_bib010) 1992; 20 Rinehart (10.1016/j.aim.2007.05.010_bib012) 1960; 27 Laville (10.1016/j.aim.2007.05.010_bib008) 1998; 8 Sudbery (10.1016/j.aim.2007.05.010_bib013) 1979; 85 Cullen (10.1016/j.aim.2007.05.010_bib003) 1965; 32 Fueter (10.1016/j.aim.2007.05.010_bib004) 1934; 7 Gentili (10.1016/j.aim.2007.05.010_bib006) 2006; 342 Kravchenko (10.1016/j.aim.2007.05.010_bib007) 1996; vol. 351 Fueter (10.1016/j.aim.2007.05.010_bib005) 1939; 12 Pogorui (10.1016/j.aim.2007.05.010_bib011) 2004; 49 Laville (10.1016/j.aim.2007.05.010_bib009) 2001; 45
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Title	A new theory of regular functions of a quaternionic variable
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